A little while back I upgraded both my iPhone 4 and iPod Touch 4 to 6.1 and then used Evasi0n and have had good success with both devices except for one single issue.

While the iPhone 4 will after screen is locked still give me WiFi access (SSH) and other methods of communication.

Yet even though I have virtually an identical configuration even Apps on the iPod Touch, I'd say 2 minutes after locking WiFi is disconnected, even if you are accessing it (you can be in SSH and just loose connection) until you unlock.

I have tried two "fixes" online such as completely reset with holding down Home + Power and setting Auto-Lock to never just locking it myself, neither has worked even though others claim it did.